text: #!/usr/bin/env python3
  # -*- coding: utf-8 -*-
  
  ## Copyright 2015-2021 PyPSA Developers
  
  ## You can find the list of PyPSA Developers at
  ## https://pypsa.readthedocs.io/en/latest/developers.html
  
  ## PyPSA is released under the open source MIT License, see
  ## https://github.com/PyPSA/PyPSA/blob/master/LICENSE.txt
  
  """
  Tools for fast Linear Problem file writing. This module contains
  
  - io functions for writing out variables, constraints and objective
    into a lp file.
  - functions to create lp format based linear expression
  - solver functions which read the lp file, run the problem and return the
    solution
  
  This module supports the linear optimal power flow calculation without using
  pyomo (see module linopt.py)
  """
  
  __author__ = "PyPSA Developers, see https://pypsa.readthedocs.io/en/latest/developers.html"
  __copyright__ = ("Copyright 2015-2021 PyPSA Developers, see https://pypsa.readthedocs.io/en/latest/developers.html, "
                   "MIT License")
  
  
  from .descriptors import Dict
  import pandas as pd
  import os
  import logging, re, io, subprocess
  import numpy as np
  from pandas import IndexSlice as idx
  from importlib.util import find_spec
  from distutils.version import LooseVersion
  
  logger = logging.getLogger(__name__)
  
  # =============================================================================
  # Front end functions
  # =============================================================================
  
  def define_variables(n, lower, upper, name, attr='', axes=None, spec='', mask=None):
      """
      Defines variable(s) for pypsa-network with given lower bound(s) and upper
      bound(s). The variables are stored in the network object under n.vars with
      key of the variable name. If multiple variables are defined at ones, at
      least one of lower and upper has to be an array (including pandas) of
      shape > (1,) or axes have to define the dimensions of the variables.
  
      Parameters
      ----------
      n : pypsa.Network
      lower : pd.Series/pd.DataFrame/np.array/str/float
          lower bound(s) for the variable(s)
      upper : pd.Series/pd.DataFrame/np.array/str/float
          upper bound(s) for the variable(s)
      name : str
          general name of the variable (or component which the variable is
          referring to). The variable will then be stored under:
  
              * n.vars[name].pnl if the variable is two-dimensional
              * n.vars[name].df if the variable is one-dimensional
  
          but can easily be accessed with :func:`get_var(n, name, attr)`
      attr : str default ''
          Specifying name of the variable, defines under which name the variable(s)
          are stored in n.vars[name].pnl if two-dimensional or in n.vars[name].df
          if one-dimensional
      axes : pd.Index or tuple of pd.Index objects, default None
          Specifies the axes and therefore the shape of the variables if bounds
          are single strings or floats. This is helpful when multiple variables
          have the same upper and lower bound.
      mask: pd.DataFrame/np.array
          Boolean mask with False values for variables which are skipped.
          The shape of the mask has to match the shape the added variables.
  
  
      Example
      --------
  
      Let's say we want to define a demand-side-managed load at each bus of
      network n, which has a minimum of 0 and a maximum of 10. We then define
      lower bound (lb) and upper bound (ub) and pass it to define_variables
  
      >>> from pypsa.linopt import define_variables, get_var
      >>> lb = pd.DataFrame(0, index=n.snapshots, columns=n.buses.index)
      >>> ub = pd.DataFrame(10, index=n.snapshots, columns=n.buses.index)
      >>> define_variables(n, lb, ub, 'DSM', 'variableload')
  
      Now the variables can be accessed by :func:`pypsa.linopt.get_var` using
  
      >>> variables = get_var(n, 'DSM', 'variableload')
  
      Note that this is usefull for the `extra_functionality` argument.
      """
      var = write_bound(n, lower, upper, axes, mask)
      set_varref(n, var, name, attr, spec=spec)
      return var
  
  
  def define_binaries(n, axes, name, attr='',  spec='', mask=None):
      """
      Defines binary-variable(s) for pypsa-network. The variables are stored
      in the network object under n.vars with key of the variable name.
      For each entry for the pd.Series of pd.DataFrame spanned by the axes
      argument the function defines a binary.
  
      Parameters
      ----------
      n : pypsa.Network
      axes : pd.Index or tuple of pd.Index objects
          Specifies the axes and therefore the shape of the variables.
      name : str
          general name of the variable (or component which the variable is
          referring to). The variable will then be stored under:
  
              * n.vars[name].pnl if the variable is two-dimensional
              * n.vars[name].df if the variable is one-dimensional
  
      attr : str default ''
          Specifying name of the variable, defines under which name the variable(s)
          are stored in n.vars[name].pnl if two-dimensional or in n.vars[name].df
          if one-dimensional
      mask: pd.DataFrame/np.array
          Boolean mask with False values for variables which are skipped.
          The shape of the mask has to match the shape given by axes.
  
      See also
      ---------
      define_variables
  
      """
      var = write_binary(n, axes)
      set_varref(n, var, name, attr, spec=spec)
      return var
  
  
  def define_constraints(n, lhs, sense, rhs, name, attr='', axes=None, spec='',
                         mask=None):
      """
      Defines constraint(s) for pypsa-network with given left hand side (lhs),
      sense and right hand side (rhs). The constraints are stored in the network
      object under n.cons with key of the constraint name. If multiple constraints
      are defined at ones, only using np.arrays, then the axes argument can be used
      for defining the axes for the constraints (this is especially recommended
      for time-dependent constraints). If one of lhs, sense and rhs is a
      pd.Series/pd.DataFrame the axes argument is not necessary.
  
      Parameters
      ----------
      n: pypsa.Network
      lhs: pd.Series/pd.DataFrame/np.array/str/float
          left hand side of the constraint(s), created with
          :func:`pypsa.linot.linexpr`.
      sense: pd.Series/pd.DataFrame/np.array/str/float
          sense(s) of the constraint(s)
      rhs: pd.Series/pd.DataFrame/np.array/str/float
          right hand side of the constraint(s), must only contain pure constants,
          no variables
      name: str
          general name of the constraint (or component which the constraint is
          referring to). The constraint will then be stored under:
  
              * n.cons[name].pnl if the constraint is two-dimensional
              * n.cons[name].df if the constraint is one-dimensional
      attr: str default ''
          Specifying name of the constraint, defines under which name the
          constraint(s) are stored in n.cons[name].pnl if two-dimensional or in
          n.cons[name].df if one-dimensional
      axes: pd.Index or tuple of pd.Index objects, default None
          Specifies the axes if all of lhs, sense and rhs are np.arrays or single
          strings or floats.
      mask: pd.DataFrame/np.array
          Boolean mask with False values for constraints which are skipped.
          The shape of the mask has to match the shape of the array that come out
          when combining lhs, sense and rhs.
  
  
      Example
      --------
  
      Let's say we want to constraint all gas generators to a maximum of 100 MWh
      during the first 10 snapshots. We then firstly get all operational variables
      for this subset and constraint there sum to less equal 100.
  
      >>> from pypsa.linopt import get_var, linexpr, define_constraints
      >>> gas_i = n.generators.query('carrier == "Natural Gas"').index
      >>> gas_vars = get_var(n, 'Generator', 'p').loc[n.snapshots[:10], gas_i]
      >>> lhs = linexpr((1, gas_vars)).sum().sum()
      >>> define_(n, lhs, '<=', 100, 'Generator', 'gas_power_limit')
  
      Now the constraint references can be accessed by
      :func:`pypsa.linopt.get_con` using
  
      >>> cons = get_var(n, 'Generator', 'gas_power_limit')
  
      Under the hood they are stored in n.cons.Generator.pnl.gas_power_limit.
      For retrieving their shadow prices add the general name of the constraint
      to the keep_shadowprices argument.
  
      Note that this is useful for the `extra_functionality` argument.
  
      """
      con = write_constraint(n, lhs, sense, rhs, axes, mask)
      set_conref(n, con, name, attr, spec=spec)
      return con
  
  # =============================================================================
  # writing functions
  # =============================================================================
  
  def _get_handlers(axes, *maybearrays):
      axes = [axes] if isinstance(axes, pd.Index) else axes
      if axes is None:
          axes, shape = broadcasted_axes(*maybearrays)
      else:
          shape = tuple(map(len, axes))
      size = np.prod(shape)
      return axes, shape, size
  
  
  def write_bound(n, lower, upper, axes=None, mask=None):
      """
      Writer function for writing out multiple variables at a time. If lower and
      upper are floats it demands to give pass axes, a tuple of (index, columns)
      or (index), for creating the variable of same upper and lower bounds.
      Return a series or frame with variable references.
      """
      axes, shape, size = _get_handlers(axes, lower, upper)
      if not size: return pd.Series(dtype=float)
      n._xCounter += size
      variables = np.arange(n._xCounter - size, n._xCounter).reshape(shape)
      lower, upper = _str_array(lower), _str_array(upper)
      exprs = lower + ' <= x' + _str_array(variables, True) + ' <= '+ upper + '\n'
      if mask is not None:
          exprs = np.where(mask, exprs, '')
          variables = np.where(mask, variables, -1)
      n.bounds_f.write(join_exprs(exprs))
      return to_pandas(variables, *axes)
  
  def write_constraint(n, lhs, sense, rhs, axes=None, mask=None):
      """
      Writer function for writing out multiple constraints to the corresponding
      constraints file. If lower and upper are numpy.ndarrays it axes must not be
      None but a tuple of (index, columns) or (index).
      Return a series or frame with constraint references.
      """
      axes, shape, size = _get_handlers(axes, lhs, sense, rhs)
      if not size: return pd.Series()
      n._cCounter += size
      cons = np.arange(n._cCounter - size, n._cCounter).reshape(shape)
      if isinstance(sense, str):
          sense = '=' if sense == '==' else sense
      lhs, sense, rhs = _str_array(lhs), _str_array(sense), _str_array(rhs)
      exprs = 'c' + _str_array(cons, True) + ':\n' + lhs + sense + ' ' + rhs + '\n\n'
      if mask is not None:
          exprs = np.where(mask, exprs, '')
          cons = np.where(mask, cons, -1)
      n.constraints_f.write(join_exprs(exprs))
      return to_pandas(cons, *axes)
  
  def write_binary(n, axes, mask=None):
      """
      Writer function for writing out multiple binary-variables at a time.
      According to the axes it writes out binaries for each entry the pd.Series
      or pd.DataFrame spanned by axes. Returns a series or frame with variable
      references.
      """
      axes, shape, size = _get_handlers(axes)
      n._xCounter += size
      variables = np.arange(n._xCounter - size, n._xCounter).reshape(shape)
      exprs = 'x' + _str_array(variables, True) + '\n'
      if mask is not None:
          exprs = np.where(mask, exprs, '')
          variables = np.where(mask, variables, -1)
      n.binaries_f.write(join_exprs(exprs))
      return to_pandas(variables, *axes)
  
  
  def write_objective(n, terms):
      """
      Writer function for writing out one or multiple objective terms.
  
      Parameters
      ----------
      n : pypsa.Network
      terms : str/numpy.array/pandas.Series/pandas.DataFrame
          String or array of strings which represent new objective terms, built
          with :func:`linexpr`
  
      """
      n.objective_f.write(join_exprs(terms))
  
  
  # =============================================================================
  # helpers, helper functions
  # =============================================================================
  
  def broadcasted_axes(*dfs):
      """
      Helper function which, from a collection of arrays, series, frames and other
      values, retrieves the axes of series and frames which result from
      broadcasting operations. It checks whether index and columns of given
      series and frames, repespectively, are aligned. Using this function allows
      to subsequently use pure numpy operations and keep the axes in the
      background.
  
      """
      axes = []
      shape = (1,)
  
      if set(map(type, dfs)) == {tuple}:
          dfs = sum(dfs, ())
  
      for df in dfs:
          shape = np.broadcast_shapes(shape, np.asarray(df).shape)
          if isinstance(df, (pd.Series, pd.DataFrame)):
              if len(axes):
                  assert (axes[-1] == df.axes[-1]).all(), ('Series or DataFrames '
                         'are not aligned. Please make sure that all indexes and '
                         'columns of Series and DataFrames going into the linear '
                         'expression are equally sorted.')
              axes = df.axes if len(df.axes) > len(axes) else axes
      return axes, shape
  
  
  def align_with_static_component(n, c, attr):
      """
      Alignment of time-dependent variables with static components. If c is a
      pypsa.component name, it will sort the columns of the variable according
      to the static component.
      """
      if c in n.all_components and (c, attr) in n.variables.index:
          if not n.variables.pnl[c, attr]: return
          if len(n.vars[c].pnl[attr].columns) != len(n.df(c).index): return
          n.vars[c].pnl[attr] = n.vars[c].pnl[attr].reindex(columns=n.df(c).index)
  
  
  def linexpr(*tuples, as_pandas=True, return_axes=False):
      """
      Elementwise concatenation of tuples in the form (coefficient, variables).
      Coefficient and variables can be arrays, series or frames. Per default
      returns a pandas.Series or pandas.DataFrame of strings. If return_axes
      is set to True the return value is split into values and axes, where values
      are the numpy.array and axes a tuple containing index and column if present.
  
      Parameters
      ----------
      tuples: tuple of tuples
          Each tuple must of the form (coeff, var), where
  
          * coeff is a numerical  value, or a numerical array, series, frame
          * var is a str or a array, series, frame of variable strings
      as_pandas : bool, default True
          Whether to return to resulting array as a series, if 1-dimensional, or
          a frame, if 2-dimensional. Supersedes return_axes argument.
      return_axes: Boolean, default False
          Whether to return index and column (if existent)
  
      Example
      -------
      Initialize coefficients and variables
  
      >>> coeff1 = 1
      >>> var1 = pd.Series(['a1', 'a2', 'a3'])
      >>> coeff2 = pd.Series([-0.5, -0.3, -1])
      >>> var2 = pd.Series(['b1', 'b2', 'b3'])
  
      Create the linear expression strings
  
      >>> linexpr((coeff1, var1), (coeff2, var2))
      0    +1.0 a1 -0.5 b1
      1    +1.0 a2 -0.3 b2
      2    +1.0 a3 -1.0 b3
      dtype: object
  
      For a further step the resulting frame can be used as the lhs of
      :func:`pypsa.linopt.define_constraints`
  
      For retrieving only the values:
  
      >>> linexpr((coeff1, var1), (coeff2, var2), as_pandas=False)
      array(['+1.0 a1 -0.5 b1', '+1.0 a2 -0.3 b2', '+1.0 a3 -1.0 b3'], dtype=object)
  
      """
      axes, shape = broadcasted_axes(*tuples)
      expr = np.repeat('', np.prod(shape)).reshape(shape).astype(object)
      if np.prod(shape):
          for coeff, var in tuples:
              newexpr = _str_array(coeff) + ' x' + _str_array(var, True) + '\n'
              if isinstance(expr, np.ndarray):
                  isna = np.isnan(coeff) | np.isnan(var) | (var == -1)
                  newexpr = np.where(isna, '', newexpr)
              expr = expr + newexpr
      if return_axes:
          return (expr, *axes)
      if as_pandas:
          return to_pandas(expr, *axes)
      return expr
  
  
  def to_pandas(array, *axes):
      """
      Convert a numpy array to pandas.Series if 1-dimensional or to a
      pandas.DataFrame if 2-dimensional. Provide index and columns if needed
      """
      return pd.Series(array, *axes) if array.ndim == 1 else pd.DataFrame(array, *axes)
  
  _to_float_str = lambda f: '%+f'%f
  _v_to_float_str = np.vectorize(_to_float_str, otypes=[object])
  
  _to_int_str = lambda d: '%d'%d
  _v_to_int_str = np.vectorize(_to_int_str, otypes=[object])
  
  def _str_array(array, integer_string=False):
      if isinstance(array, (float, int)):
          if integer_string:
              return _to_int_str(array)
          return _to_float_str(array)
      array = np.asarray(array)
      if array.dtype.type == np.str_:
          array = np.asarray(array, dtype=object)
      if array.dtype < str and array.size:
          if integer_string:
              array = np.nan_to_num(array, False, -1)
              return _v_to_int_str(array)
          return _v_to_float_str(array)
      else:
          return array
  
  def join_exprs(df):
      """
      Helper function to join arrays, series or frames of strings together.
  
      """
      return ''.join(np.asarray(df).flatten())
  
  # =============================================================================
  #  references to vars and cons, rewrite this part to not store every reference
  # =============================================================================
  
  def _add_reference(ref_dict, df, attr, pnl=True):
      if pnl:
          if attr in ref_dict.pnl:
              ref_dict.pnl[attr][df.columns] = df
          else:
              ref_dict.pnl[attr] = df
      else:
          if attr in ref_dict.df:
              ref_dict.df = pd.concat([ref_dict.df, df.to_frame(attr)])
          else:
              ref_dict.df[attr] = df
  
  
  def set_varref(n, variables, c, attr, spec=''):
      """
      Sets variable references to the network.
      One-dimensional variable references will be collected at `n.vars[c].df`,
      two-dimensional varaibles in `n.vars[c].pnl`. For example:
  
      * nominal capacity variables for generators are stored in
        `n.vars.Generator.df.p_nom`
      * operational variables for generators are stored in
        `n.vars.Generator.pnl.p`
      """
      if not variables.empty:
          pnl = variables.ndim == 2
          if c not in n.variables.index:
              n.vars[c] = Dict(df=pd.DataFrame(), pnl=Dict())
          if ((c, attr) in n.variables.index) and (spec != ''):
              n.variables.at[idx[c, attr], 'specification'] += ', ' + spec
          else:
              n.variables.loc[idx[c, attr], :] = [pnl, spec]
          _add_reference(n.vars[c], variables, attr, pnl=pnl)
  
  def set_conref(n, constraints, c, attr, spec=''):
      """
      Sets constraint references to the network.
      One-dimensional constraint references will be collected at `n.cons[c].df`,
      two-dimensional in `n.cons[c].pnl`
      For example:
  
      * constraints for nominal capacity variables for generators are stored in
        `n.cons.Generator.df.mu_upper`
      * operational capacity limits for generators are stored in
        `n.cons.Generator.pnl.mu_upper`
      """
      if not constraints.empty:
          pnl = constraints.ndim == 2
          if c not in n.constraints.index:
              n.cons[c] = Dict(df=pd.DataFrame(), pnl=Dict())
          if ((c, attr) in n.constraints.index) and (spec != ''):
              n.constraints.at[idx[c, attr], 'specification'] += ', ' + spec
          else:
              n.constraints.loc[idx[c, attr], :] = [pnl, spec]
          _add_reference(n.cons[c], constraints, attr, pnl=pnl)
  
  def get_var(n, c, attr, pop=False):
      """
      Retrieves variable references for a given static or time-depending
      attribute of a given component. The function looks into n.variables to
      detect whether the variable is a time-dependent or static.
  
      Parameters
      ----------
      n : pypsa.Network
      c : str
          component name to which the constraint belongs
      attr: str
          attribute name of the constraints
  
      Example
      -------
      >>> get_var(n, 'Generator', 'p')
  
      """
      vvars = n.vars[c].pnl if n.variables.pnl[c, attr] else n.vars[c].df
      return vvars.pop(attr) if pop else vvars[attr]
  
  
  def get_con(n, c, attr, pop=False):
      """
      Retrieves constraint references for a given static or time-depending
      attribute of a give component.
  
      Parameters
      ----------
      n : pypsa.Network
      c : str
          component name to which the constraint belongs
      attr: str
          attribute name of the constraints
  
      Example
      -------
      get_con(n, 'Generator', 'mu_upper')
      """
      cons = n.cons[c].pnl if n.constraints.pnl[c, attr] else n.cons[c].df
      return cons.pop(attr) if pop else cons[attr]
  
  
  def get_sol(n, name, attr=''):
      """
      Retrieves solution for a given variable. Note that a lookup of all stored
      solutions is given in n.solutions.
  
  
      Parameters
      ----------
      n : pypsa.Network
      c : str
          general variable name (or component name if variable is attached to a
          component)
      attr: str
          attribute name of the variable
  
      Example
      -------
      get_dual(n, 'Generator', 'mu_upper')
      """
      pnl = n.solutions.at[(name, attr), 'pnl']
      if n.solutions.at[(name, attr), 'in_comp']:
          return n.pnl(name)[attr] if pnl else n.df(name)[attr + '_opt']
      else:
          return n.sols[name].pnl[attr] if pnl else n.sols[name].df[attr]
  
  
  def get_dual(n, name, attr=''):
      """
      Retrieves shadow price for a given constraint. Note that for retrieving
      shadow prices of a custom constraint, its name has to be passed to
      `keep_references` in the lopf, or `keep_references` has to be set to True.
      Note that a lookup of all stored shadow prices is given in n.dualvalues.
  
      Parameters
      ----------
      n : pypsa.Network
      c : str
          constraint name to which the constraint belongs
      attr: str
          attribute name of the constraints
  
      Example
      -------
      get_dual(n, 'Generator', 'mu_upper')
      """
      pnl = n.dualvalues.at[(name, attr), 'pnl']
      if n.dualvalues.at[(name, attr), 'in_comp']:
          return n.pnl(name)[attr] if pnl else n.df(name)[attr]
      else:
          return n.duals[name].pnl[attr] if pnl else n.duals[name].df[attr]
  
  
  # =============================================================================
  # solvers
  # =============================================================================
  
  def set_int_index(ser):
      ser.index = ser.index.str[1:].astype(int)
      return ser
  
  
  def run_and_read_highs(n, problem_fn, solution_fn, solver_logfile,
                          solver_options={}, warmstart=None, store_basis=True):
      """
      Highs solver function. Reads a linear problem file and passes it to the highs
      solver. If the solution is feasible the function returns the objective,
      solution and dual constraint variables. Highs must be installed for usage.
      Documentation: https://www.maths.ed.ac.uk/hall/HiGHS/
  
      Notes
      -----
      
      The script might only work for version HiGHS 1.1.1. Installation steps::
          sudo apt-get install cmake  # if not installed
          git clone git@github.com:ERGO-Code/HiGHS.git
          cd HiGHS
          git checkout 95342daa73543cc21e5b27db3e0fbf7330007541 # moves to HiGHS 1.1.1
          mkdir build
          cd build
          cmake ..
          make
          ctest
  
      Then in .bashrc add paths of executables and library ::
          export PATH="${PATH}:/foo/HiGHS/build/bin"
          export LD_LIBRARY_PATH="${LD_LIBRARY_PATH}:/foo/HiGHS/build/lib"
          source .bashrc
  
      Now when typing ``highs`` in the terminal you should see something like ::
          Running HiGHS 1.1.1 [date: 2021-11-14, git hash: 95342daa]
  
      The function reads and execute (i.e. subprocess.Popen,...) terminal
      commands of the solver. Meaning the command can be also executed at your
      command window/terminal if HiGHs is installed. Executing the commands on
      your local terminal helps to identify the raw outputs that are useful for
      developing the interface further.
  
      All functions below the "process = ..." do only read and save the outputs
      generated from the HiGHS solver. These parts are solver specific and
      depends on the solver output.
  
      Solver options are read by the 1) command window and the 2) option_file.txt
  
      1) An example list of solver options executable by the command window is given here:
      Examples:
      --model_file arg 	File of model to solve.
      --presolve arg 	    Presolve: "choose" by default - "on"/"off" are alternatives.
      --solver arg 	    Solver: "choose" by default - "simplex"/"ipm" are alternatives.
      --parallel arg 	    Parallel solve: "choose" by default - "on"/"off" are alternatives.
      --time_limit arg 	Run time limit (double).
      --options_file arg 	File containing HiGHS options.
      -h, --help 	        Print help.
  
      2) The options_file.txt gives some more options, see a full list here:
      https://www.maths.ed.ac.uk/hall/HiGHS/HighsOptions.set
      By default, we insert a couple of options for the ipm solver. The dictionary
      can be overwritten by simply giving the new values. For instance, you could
      write a dictionary replacing some of the default values or adding new options:
  
      ```
      solver_options = {
          name: highs,
          method: ipm,
          parallel: "on",
          <option_name>: <value>,
      }
      ```
  
      Note, the <option_name> and <value> must be equivalent to the name convention
      of HiGHS. Some function exist that are not documented, check their GitHub file:
      https://github.com/ERGO-Code/HiGHS/blob/master/src/lp_data/HighsOptions.h
  
      Returns
      -------
  
      status : string,
          "ok" or "warning"
      termination_condition : string,
          Contains "optimal", "infeasible",
      variables_sol : series
      constraints_dual : series
      objective : float
  
      """
      logger.warning("The HiGHS solver can potentially solve towards variables that slightly deviate from Gurobi,cbc,glpk")
      options_fn = "highs_options.txt"
      default_dict = {
          "method": "ipm",
          "primal_feasibility_tolerance": 1e-04,
          "dual_feasibility_tolerance": 1e-05,
          "ipm_optimality_tolerance": 1e-6,
          "presolve": "on",
          "run_crossover": True,
          "parallel": "off",
          "threads": 4,
          "solution_file": solution_fn,
          "write_solution_to_file": True,
          "write_solution_style": 1,
          "log_to_console": True,
      }
      # update default_dict through solver_options and write to file
      default_dict.update(solver_options)
      method = default_dict.pop("method", "ipm")
      logger.info(f"Options: \"{default_dict}\". List of options: https://www.maths.ed.ac.uk/hall/HiGHS/HighsOptions.set")
      f1 = open(options_fn, "w")
      f1.write('\n'.join([f"{k} = {v}" for k, v in default_dict.items()]))
      f1.close()
  
      # write (terminal) commands
      command = f"highs --model_file {problem_fn} "
      if warmstart:
          logger.warning("Warmstart, not available in HiGHS. Will be ignored.")
      command += f"--solver {method} --options_file {options_fn}"
      logger.info(f"Solver command: \"{command}\"")
      # execute command and store command window output
      process = subprocess.Popen(
          command.split(' '),
          stdout=subprocess.PIPE,
          universal_newlines=True
      )
  
      def read_until_break():
          # Function that reads line by line the command window
          while True:
              out = process.stdout.readline(1)
              if out == '' and process.poll() != None:
                  break
              if out != '':
                  yield out
  
      # converts stdout (standard terminal output) to pandas dataframe
      log = io.StringIO(''.join(read_until_break())[:])
      log = pd.read_csv(log, sep=':', index_col=0, header=None)[1].squeeze()
      if solver_logfile is not None:
          log.to_csv(solver_logfile, sep="\t")
      log.index = log.index.str.strip()
      os.remove(options_fn)
  
      # read out termination_condition from `info`
      model_status = log["Model   status"].strip().lower()
      if "optimal" in model_status:
          status = "ok"
          termination_condition = model_status
      elif "infeasible" in model_status:
          status = "warning"
          termination_condition = model_status
      else:
          status = 'warning'
          termination_condition = model_status
      objective = float(log["Objective value"])
  
      # read out solution file (.sol)
      f = open(solution_fn, "rb")
      trimed_sol_fn = re.sub(rb'\*\*\s+', b'', f.read())
      f.close()
  
      sol = pd.read_csv(io.BytesIO(trimed_sol_fn), header=[1], sep=r'\s+')
      row_no = sol[sol["Index"] == 'Rows'].index[0]
      sol = sol.drop(row_no+1)  # Removes header line after "Rows"
      sol_rows = sol[(sol.index > row_no)]
      sol_cols = sol[(sol.index < row_no)].set_index("Name").pipe(set_int_index)
      variables_sol = pd.to_numeric(sol_cols["Primal"], errors="raise")
      constraints_dual = pd.to_numeric(sol_rows["Dual"], errors="raise").reset_index(drop=True)
      constraints_dual.index += 1
  
      return (status, termination_condition, variables_sol,
              constraints_dual, objective)
  
  
  def run_and_read_cbc(n, problem_fn, solution_fn, solver_logfile,
                       solver_options, warmstart=None, store_basis=True):
      """
      Solving function. Reads the linear problem file and passes it to the cbc
      solver. If the solution is successful it returns variable solutions and
      constraint dual values.
  
      For more information on the solver options, run 'cbc' in your shell
      """
      with open(problem_fn, 'rb') as f:
          for str in f.readlines():
              assert (("> " in str.decode('utf-8')) == False), (">, must be"
                      "changed to >=")
              assert (("< " in str.decode('utf-8')) == False), ("<, must be"
                      "changed to <=")
  
      #printingOptions is about what goes in solution file
      command = f"cbc -printingOptions all -import {problem_fn} "
      if warmstart:
          command += f'-basisI {warmstart} '
      if (solver_options is not None) and (solver_options != {}):
          command += solver_options
      command += f"-solve -solu {solution_fn} "
      if store_basis:
          n.basis_fn = solution_fn.replace('.sol', '.bas')
          command += f'-basisO {n.basis_fn} '
  
      if not os.path.exists(solution_fn):
          os.mknod(solution_fn)
  
      log = open(solver_logfile, 'w') if solver_logfile is not None else subprocess.PIPE
      result = subprocess.Popen(command.split(' '), stdout=log)
      result.wait()
  
      with open(solution_fn, "r") as f:
          data = f.readline()
  
  
      if data.startswith("Optimal - objective value"):
          status = "ok"
          termination_condition = "optimal"
          objective = float(data[len("Optimal - objective value "):])
      elif "Infeasible" in data:
          status = "warning"
          termination_condition = "infeasible"
      else:
          status = 'warning'
          termination_condition = "other"
  
      if termination_condition != "optimal":
          return status, termination_condition, None, None, None
  
      f = open(solution_fn,"rb")
      trimed_sol_fn = re.sub(rb'\*\*\s+', b'', f.read())
      f.close()
  
      sol = pd.read_csv(io.BytesIO(trimed_sol_fn), header=None, skiprows=[0],
                        sep=r'\s+', usecols=[1,2,3], index_col=0)
      variables_b = sol.index.str[0] == 'x'
      variables_sol = sol[variables_b][2].pipe(set_int_index)
      constraints_dual = sol[~variables_b][3].pipe(set_int_index)
      return (status, termination_condition, variables_sol,
              constraints_dual, objective)
  
  
  def run_and_read_glpk(n, problem_fn, solution_fn, solver_logfile,
                       solver_options, warmstart=None, store_basis=True):
      """
      Solving function. Reads the linear problem file and passes it to the glpk
      solver. If the solution is successful it returns variable solutions and
      constraint dual values.
  
      For more information on the glpk solver options:
      https://kam.mff.cuni.cz/~elias/glpk.pdf
      """
      # TODO use --nopresol argument for non-optimal solution output
      command = (f"glpsol --lp {problem_fn} --output {solution_fn}")
      if solver_logfile is not None:
          command += f' --log {solver_logfile}'
      if warmstart:
          command += f' --ini {warmstart}'
      if store_basis:
          n.basis_fn = solution_fn.replace('.sol', '.bas')
          command += f' -w {n.basis_fn}'
      if (solver_options is not None) and (solver_options != {}):
          command += solver_options
  
      result = subprocess.Popen(command.split(' '), stdout=subprocess.PIPE)
      result.wait()
  
      f = open(solution_fn)
      def read_until_break(f):
          linebreak = False
          while not linebreak:
              line = f.readline()
              linebreak = line == '\n'
              yield line
  
      info = io.StringIO(''.join(read_until_break(f))[:-2])
      info = pd.read_csv(info, sep=':',  index_col=0, header=None)[1]
      termination_condition = info.Status.lower().strip()
      objective = float(re.sub(r'[^0-9\.\+\-e]+', '', info.Objective))
  
      if termination_condition in ["optimal","integer optimal"]:
          status = "ok"
          termination_condition = "optimal"
      elif termination_condition == "undefined":
          status = "warning"
          termination_condition = "infeasible"
      else:
          status = "warning"
  
      if termination_condition != 'optimal':
          return status, termination_condition, None, None, None
  
      duals = io.StringIO(''.join(read_until_break(f))[:-2])
      duals = pd.read_fwf(duals)[1:].set_index('Row name')
      if 'Marginal' in duals:
          constraints_dual = pd.to_numeric(duals['Marginal'], 'coerce')\
                                .fillna(0).pipe(set_int_index)
      else:
          logger.warning("Shadow prices of MILP couldn't be parsed")
          constraints_dual = pd.Series(index=duals.index, dtype=float)
  
      sol = io.StringIO(''.join(read_until_break(f))[:-2])
      variables_sol = (pd.read_fwf(sol)[1:].set_index('Column name')
                       ['Activity'].astype(float).pipe(set_int_index))
      f.close()
  
      return (status, termination_condition, variables_sol,
              constraints_dual, objective)
  
  
  def run_and_read_cplex(n, problem_fn, solution_fn, solver_logfile,
                          solver_options, warmstart=None, store_basis=True):
      """
      Solving function. Reads the linear problem file and passes it to the cplex
      solver. If the solution is successful it returns variable solutions and
      constraint dual values. Cplex must be installed for using this function
  
      """
      if find_spec('cplex') is None:
          raise ModuleNotFoundError("Optional dependency 'cplex' not found."
             "Install via 'conda install -c ibmdecisionoptimization cplex' "
             "or 'pip install cplex'")
      import cplex
      _version = LooseVersion(cplex.__version__)
      m = cplex.Cplex()
      if solver_logfile is not None:
          if _version >= "12.10":
              log_file_or_path = open(solver_logfile, "w")
          else:
              log_file_or_path = solver_logfile
          m.set_log_stream(log_file_or_path)
      if solver_options is not None:
          for key, value in solver_options.items():
              param = m.parameters
              for key_layer in key.split("."):
                  param = getattr(param, key_layer)
              param.set(value)
      m.read(problem_fn)
      if warmstart:
          m.start.read_basis(warmstart)
      m.solve()
      is_lp = m.problem_type[m.get_problem_type()] == 'LP'
      if solver_logfile is not None:
          if isinstance(log_file_or_path, io.IOBase):
              log_file_or_path.close()
  
      termination_condition = m.solution.get_status_string()
      if 'optimal' in termination_condition:
          status = 'ok'
          termination_condition = 'optimal'
      else:
          status = 'warning'
  
      if (status == 'ok') and store_basis and is_lp:
          n.basis_fn = solution_fn.replace('.sol', '.bas')
          try:
              m.solution.basis.write(n.basis_fn)
          except cplex.exceptions.errors.CplexSolverError:
              logger.info('No model basis stored')
              del n.basis_fn
  
      objective = m.solution.get_objective_value()
      variables_sol = pd.Series(m.solution.get_values(), m.variables.get_names())\
                        .pipe(set_int_index)
      if is_lp:
          constraints_dual = pd.Series(m.solution.get_dual_values(),
                           m.linear_constraints.get_names()).pipe(set_int_index)
      else:
          logger.warning("Shadow prices of MILP couldn't be parsed")
          constraints_dual = pd.Series(index=m.linear_constraints.get_names())\
                               .pipe(set_int_index)
      del m
      return (status, termination_condition, variables_sol, constraints_dual,
              objective)
  
  
  def run_and_read_gurobi(n, problem_fn, solution_fn, solver_logfile,
                          solver_options, warmstart=None, store_basis=True):
      """
      Solving function. Reads the linear problem file and passes it to the gurobi
      solver. If the solution is successful it returns variable solutions and
      constraint dual values. Gurobipy must be installed for using this function
  
      For more information on solver options:
      https://www.gurobi.com/documentation/{gurobi_verion}/refman/parameter_descriptions.html
      """
      if find_spec('gurobipy') is None:
          raise ModuleNotFoundError("Optional dependency 'gurobipy' not found. "
             "Install via 'conda install -c gurobi gurobi'  or follow the "
             "instructions on the documentation page "
             "https://www.gurobi.com/documentation/")
      import gurobipy
      # disable logging for this part, as gurobi output is doubled otherwise
      logging.disable(50)
  
      m = gurobipy.read(problem_fn)
      if solver_options is not None:
          for key, value in solver_options.items():
              m.setParam(key, value)
      if solver_logfile is not None:
          m.setParam("logfile", solver_logfile)
  
      if warmstart:
          m.read(warmstart)
      m.optimize()
      logging.disable(1)
  
      if store_basis:
          n.basis_fn = solution_fn.replace('.sol', '.bas')
          try:
              m.write(n.basis_fn)
          except gurobipy.GurobiError:
              logger.info('No model basis stored')
              del n.basis_fn
  
      Status = gurobipy.GRB.Status
      statusmap = {getattr(Status, s) : s.lower() for s in Status.__dir__()
                                                  if not s.startswith('_')}
      termination_condition = statusmap[m.status]
  
      if termination_condition == "optimal":
          status = 'ok'
      elif termination_condition == 'suboptimal':
          status = 'warning'
      elif termination_condition == "infeasible":
          status = 'warning'
      elif termination_condition == "inf_or_unbd":
          status = 'warning'
          termination_condition = "infeasible or unbounded"
      else:
          status = "warning"
  
      if termination_condition not in ["optimal","suboptimal"]:
          return status, termination_condition, None, None, None
  
      variables_sol = pd.Series({v.VarName: v.x for v
                                 in m.getVars()}).pipe(set_int_index)
      try:
          constraints_dual = pd.Series({c.ConstrName: c.Pi for c in
                                        m.getConstrs()}).pipe(set_int_index)
      except AttributeError:
          logger.warning("Shadow prices of MILP couldn't be parsed")
          constraints_dual = pd.Series(index=[c.ConstrName for c in m.getConstrs()])
      objective = m.ObjVal
      del m
      return (status, termination_condition, variables_sol,
              constraints_dual, objective)
  
  
  def run_and_read_xpress(n, problem_fn, solution_fn, solver_logfile,
                          solver_options, keep_files, warmstart=None,
                          store_basis=True):
      """
      Solving function. Reads the linear problem file and passes it to
      the Xpress solver. If the solution is successful it returns
      variable solutions and constraint dual values. The xpress module
      must be installed for using this function.
  
      For more information on solver options:
      https://www.fico.com/fico-xpress-optimization/docs/latest/solver/GUID-ACD7E60C-7852-36B7-A78A-CED0EA291CDD.html
      """
  
      import xpress
  
      m = xpress.problem()
  
      m.read(problem_fn)
      m.setControl(solver_options)
  
      if solver_logfile is not None:
          m.setlogfile(solver_logfile)
  
      if warmstart:
          m.readbasis(warmstart)
  
      m.solve()
  
      if store_basis:
          n.basis_fn = solution_fn.replace('.sol', '.bas')
          try:
              m.writebasis(n.basis_fn)
          except:
              logger.info('No model basis stored')
              del n.basis_fn
  
      termination_condition = m.getProbStatusString()
  
      if termination_condition == 'mip_optimal' or \
         termination_condition == 'lp_optimal':
          status = 'ok'
          termination_condition = 'optimal'
      elif termination_condition == 'mip_unbounded' or \
           termination_condition == 'mip_infeasible' or \
           termination_condition == 'lp_unbounded' or \
           termination_condition == 'lp_infeasible':
          status = 'infeasible or unbounded'
      else:
          status = 'warning'
  
      if termination_condition not in ["optimal"]:
          return status, termination_condition, None, None, None
  
      var = [str(v) for v in m.getVariable()]
      variables_sol = pd.Series(m.getSolution(var), index=var).pipe(set_int_index)
  
      try:
          dual = [str(d) for d in m.getConstraint()]
          constraints_dual = pd.Series(m.getDual(dual), index=dual).pipe(set_int_index)
      except xpress.SolverError:
          logger.warning("Shadow prices of MILP couldn't be parsed")
          constraints_dual = pd.Series(index=dual).pipe(set_int_index)
  
      objective = m.getObjVal()
  
      del m
  
      return (status, termination_condition, variables_sol,
              constraints_dual, objective)
  